Question: $\begin{cases}a(1)=\dfrac{5}{3}\\\\ a(n)=a(n-1)\cdot (-9) \end{cases}$ What is the $3^{\text{rd}}$ term in the sequence?
Answer: This is a recursive formula. It tells us that the first term is $\dfrac{5}{3}$ and that the common ratio is $-9$. $\begin{aligned} {a(1)}&=\dfrac{5}{3} \\\\ {a(2)}&={a(1)}\cdot (-9)=-15 \\\\ {a(3)}&={a(2)}\cdot (-9)=135 \end{aligned}$ The $3^{\text{rd}}$ term is $135$.